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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.28507 |
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| _version_ | 1866913168237789184 |
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| author | Berndt, Torben Farjallah, Elyes Seute, Leif Saqur, Raeid Walker, Benjamin Stühmer, Jan |
| author_facet | Berndt, Torben Farjallah, Elyes Seute, Leif Saqur, Raeid Walker, Benjamin Stühmer, Jan |
| contents | Recent work on the sequence universality of State Space Models (SSMs) has introduced efficient, maximally expressive continuous-time approaches for time-series modelling. While these works focus on discriminative settings, we extend this perspective to generative time-series modelling by proving that maximally expressive Structured Linear Controlled Differential Equations (SLiCEs) are universal time-series generators, in the sense that they can approximate the induced path laws of continuous causal pushforwards on compact latent sets in $W_\infty$. Building on these theoretical results, we propose Generative SLiCEs (G-SLiCEs), a maximally expressive continuous-time model for flow matching on path-space. Empirically, we show that expressivity improves performance in probabilistic forecasting and downstream tasks, while retaining the advantages of continuous-time models such as generalising to arbitrary observation grids. This is particularly beneficial for irregular grids, where fixed-grid models often struggle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28507 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Universal Time Series Generation with Neural Controlled Differential Equations Berndt, Torben Farjallah, Elyes Seute, Leif Saqur, Raeid Walker, Benjamin Stühmer, Jan Machine Learning Recent work on the sequence universality of State Space Models (SSMs) has introduced efficient, maximally expressive continuous-time approaches for time-series modelling. While these works focus on discriminative settings, we extend this perspective to generative time-series modelling by proving that maximally expressive Structured Linear Controlled Differential Equations (SLiCEs) are universal time-series generators, in the sense that they can approximate the induced path laws of continuous causal pushforwards on compact latent sets in $W_\infty$. Building on these theoretical results, we propose Generative SLiCEs (G-SLiCEs), a maximally expressive continuous-time model for flow matching on path-space. Empirically, we show that expressivity improves performance in probabilistic forecasting and downstream tasks, while retaining the advantages of continuous-time models such as generalising to arbitrary observation grids. This is particularly beneficial for irregular grids, where fixed-grid models often struggle. |
| title | Universal Time Series Generation with Neural Controlled Differential Equations |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.28507 |